About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

In cell biology and other fields the automatic accurate localization of sub-resolution objects in
images is an important tool. The signal is often corrupted by multiple forms of noise, including
excess noise resulting from the amplification by an electron multiplying charge-coupled device
(EMCCD). Here we present our novel Nested Maximum Likelihood Algorithm (NMLA), which solves the
problem of localizing multiple overlapping emitters in a setting affected by excess noise, by
repeatedly solving the task of independent localization for single emitters in an excess noise-free
system. NMLA dramatically improves scalability and robustness, when compared to a general purpose
optimization technique. Our method was successfully applied for in vivo
localization of fluorescent proteins.

Figures (4)

Fig. 1 The NMLA tracks proteins in vivo (a) Image of a fission yeast cell expressing
dynein heavy chain tagged with 3 GFPs (Dhc1-3GFP). The white line marks the cell outline, the green
arrowhead marks a dynein molecule. The brightest spot is the spindle pole body. (b) The movement of
dyneins is visualized in consecutive maximum intensity projections onto the y-axis (see color bar).
(c) Schematic representation of the NMLA. The outer loop, which addresses the excess noise, is
depicted in blue while the inner loop, which performs the localization, is depicted in gray. (d)
Scheme of cell with the 2D trace of a dynein (green, corresponding to the green arrowhead in a)
tracked using the NMLA. (e) Projection onto the y-axis of the traces obtained using the NMLA. The
green trace is the path of the molecule marked in a.

Fig. 2 The NMLA and its inner loop closely approach the theoretical bounds in simulation. (a) The
standard deviation of the localization results in one dimension as a function of the flux of the
blob. The complete NMLA (red squares) and the inner loop (red triangles) were applied to the
simulated images. The inner loop was also applied to the same image series without excess noise
(blue triangles). The results are compared with theoretical bounds: the Cramer-Rao lower bound
(CRLB) for a scenario without excess noise (blue line), the CRLB considering excess noise (red line)
and the approximated bound suggested in [13]
(black line). The NMLA yields the highest possible precision, given by the CRLB, in settings with
excess noise. (b) The standard deviation of the localization results as a function of background
flux. The flux of the blob was set to 25 photons. The remaining parameters and the algorithms
employed were as in a. Note that the deviation between the theoretical bounds and the results of the
estimators (also seen in [23]) is a general
feature of the ML localization. In a and b, simulated images (without excess noise outlined in blue,
and the same image with excess noise outlined in red) correspond to different values of
flux/background flux indicated by the dashed lines under the images. In the images without excess
noise the colors indicate the number of photons in each pixel. In the images with excess noise
colors indicate the estimated number of photons as described in the Appendix.

Fig. 3 The standard deviation of the localization results as a function of the measured flux of
fluorescent bead images. Three 3000-frame-long movies were obtained using Total Internal Reflection
Fluorescence (TIRF) microscopy with different laser powers and EMCCD gain of 300. The pixel size was
106 nm (see Appendix for details). The beads were localized
with the NMLA (squares) and its inner loop (triangles). Each pair of a triangle and a square at a
certain value of flux corresponds to a single bead; displayed are images of three tracked beads
connected to their resulting data point. The results are compared with the CRLB considering excess
noise. The background flux used in the calculation of the bound was derived from the average
intensities in manually selected empty areas of the movies (see Appendix for details). The inset is an enlarged view of the section corresponding to the low
flux region (dashed lines) including the theoretical bound from [13].

Fig. 4 Th NMLA outperforms Powell’s method with regard to scalability and robustness. (a)
Required computation time as a function of the number of emitters. Different numbers of overlapping
emitters were tracked with three different implementations of the excess noise aware ML estimator:
The computation time required by Powell’s method (circles) grows significantly faster than
the time required by the NMLA (squares). A naively parallelized version of the NMLA (diamonds)
yields a further improvement. (b) Number of inliers in localization results as a function of the
standard deviation of the random initialization. In each frame the algorithms were initialized at a
Gaussian distributed random location around the true position of the emitter. Every location
estimate closer than 1.3 pixels to the correct location was considered an inlier. The NMLA achieves
100% inliers for higher standard deviations and does not loose as many as Powell’s
method.